Find all solutions of the system where is a parameter.
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Find all solutions $x_1, x_2, x_3, x_4, x_5$ of the system $$x_5+x_2=yx_1$$ $$x_1+x_3=yx_2$$ $$x_2+x_4=yx_3$$ $$x_3+x_5=yx_4$$ $$x_4+x_1=yx_5$$ where $y$ is a parameter.
Source: Međunarodna matematička olimpijada, shortlist 1963
Školjka 
of the system 
where 
is a parameter.